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2n +1 1. Let an = for each n E N. Vn2 +1 (a) Prove that (an) → 2 using the definition of convergence (i.e., from first principles using e, N). (b) Deduce from your proof an integer N EN such that an E (1.9, 2.1) for all n > N. Verify this by computing an to 2 decimal places. (You may use a calculator.)

2n +1 1. Let an = for each n E N. Vn2 +1 (a) Prove that (an) → 2 using the definition of convergence (i.e., from first principles using e, N). (b) Deduce from your proof an integer N EN such that an E (1.9, 2.1) for all n > N. Verify this by computing an to 2 decimal places. (You may use a calculator.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2n +1 1. Let an = for each n E N. Vn2 + 1 (a) Prove that (am) → 2 using the definition of convergence (i.e., from first principles using e, N). (b) Deduce from your proof an integer N E N such that an E (1.9, 2.1) for all n > N. Verify this by computing an to 2 decimal places. (You may use a calculator.) 2. The Fibonacci sequence 1, 1,2, 3, 5, ... is the sequence (fn)nɛN defined by fi = 1, f2 = 1, and fn = fn-1+ fn-2 if n > 3. The aim of this quostion is to provo that the soquonco (a )of rational numbors a f
Transcribed Image Text:2n +1 1. Let an = for each n E N. Vn2 + 1 (a) Prove that (am) → 2 using the definition of convergence (i.e., from first principles using e, N). (b) Deduce from your proof an integer N E N such that an E (1.9, 2.1) for all n > N. Verify this by computing an to 2 decimal places. (You may use a calculator.) 2. The Fibonacci sequence 1, 1,2, 3, 5, ... is the sequence (fn)nɛN defined by fi = 1, f2 = 1, and fn = fn-1+ fn-2 if n > 3. The aim of this quostion is to provo that the soquonco (a )of rational numbors a f
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